Todd Frazier was the third piece in a three-player package the Yankees received in July, present as much because the White Sox wanted to unload the rest of his salary as the Yankees hungered for his inclusion.

Tommy Kahnle was priority one for the Yankees, David Robertson the second key, both made more attractive because they were controlled through at least next season while Frazier was in his walk year.

The trade, in the short run, has worked out well for the Yankees, as all three have played well, with Frazier providing benefits perhaps only a team that has him can fully appreciate — his passion, confidence, high baseball IQ and fearlessness in huge spots elevating his overall value.

“I am glad I had the opportunity to see what he brings to the table,” Bryan Price, Frazier’s manager in Cincinnati in 2014-15, said by phone. “He is coming up on free agency and his batting average is not as robust as some might like, but if you take a hard look at his intangibles, you get a better player than the numbers suggest. For example, he’s not afraid to be in the big moment, in fact, I think he embraces it.”

Frazier’s free agency takes on further intrigue around here because there are scenarios in which the Yankees retain him, but there’s a good case for why he might be even a better fit for the Mets.

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Frazier does what Sandy Alderson likes in a hitter — he draws walks (career-high 83 this year) and hits homers (131 over the last four years, ninth most in the majors), which help nullify some of the impact of low batting averages since his OPS continues to be above league average. In addition, the Mets want to upgrade their defense, and Frazier would be significantly better than who played there last year for the Mets, even as they liked Asdrubal Cabrera’s transition to third.

And the Mets also are trying — once again — to address their culture. Frazier is a baseball gym rat, endlessly enthusiastic about the game, willing to be a spokesman, a well-regarded teammate. His three-run homer in the second inning of ALCS Game 2 Monday night sent the Yankees toward an 8-1 victory, and afterward Frazier’s joy at a postgame press conference was overt. He was bubbling as much as speaking, expressing the never-lost exuberance of a child for being in this place in this time, all of it made better because he is a Jersey kid who grew up a Yankee fan.

“That is not contrived, he is very authentic,” Price said. “No matter how much he might struggle at the plate, his love for the game is always there, and his passion to figure out ways for his team to win never goes away.”

Frazier hit 27 homers, but that he is 31st in Wins Above Replacement in the same timeframe shows the value of his all-around game. Since he does not turn 32 until February, Frazier almost certainly will pursue a multi-year deal. That probably will deter the Yankees, who have Gleyber Torres and Miguel Andujar close to the majors, still have Chase Headley’s $13 million contract next year and are trying to get under the luxury tax in 2018. Frazier might have a role as a third baseman/first baseman/DH with the Yanks, but it is hard to envision them bringing him back unless they moved Headley — and perhaps not even then.

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Will the Mets, looking to cut payroll, also be scared of the price tag? Frazier gives the advantage of also being able to move to first base if there is a baseball miracle and David Wright returns or if Dominic Smith needs further minor league seasoning.

There also is a question of the allure of playing close to home — Frazier has spoken openly of how much that has added to his fun. Would he be willing to accept less to stay in New York or go to Philadelphia over joining clubs that need a third baseman, such as the Angels, Braves or Giants?

Also, many position players had difficulty landing multiple-year pacts last offseason. And you wonder if Frazier’s unorthodox swing and steadily declining batting averages scare potential suitors.

That Frazier is good on both sides of the ball should help his marketability — his 3.4 WAR in 2017 was the same as Robinson Cano’s and better than players such as Daniel Murphy and Jay Bruce. Plus, Frazier carries himself like someone better than his skills, which makes him like bright lights, big cities and huge spots.

“He pitched and hit to help Toms River win the Little League World Series, and it is like he transitioned his confidence from there to our ball club,” Price said. “He just emanated unbelievable confidence like that 12-year-old regardless of how great the velocity became in the majors or how hard balls were hit to him at third base. Nothing discourages him. Nothing makes him lose confidence that he is a really good baseball player and a difference-maker.”